In this article, a posteriori error estimates are derived for mixed finite element Galerkin approximations to second order linear parabolic initial and boundary value problems. Using mixed elliptic reconstructions, a posteriori error estimates in L∞(L2)- and L2(L2)-norms for the solution as well as its flux are proved for the semidiscrete scheme. Finally, based on a backward Euler method, a completely discrete scheme is analyzed and a posteriori error bounds are derived, which improves upon earlier results on a posteriori estimates of mixed finite element approximations to parabolic problems. Results of numerical experiments verifying the efficiency of the estimators have also been provided. © 2012 Society for Industrial and Applied Mathematics.
|Original language||English (US)|
|Number of pages||27|
|Journal||SIAM Journal on Numerical Analysis|
|State||Published - Jan 2012|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: Received by the editors January 15, 2010; accepted for publication (in revised form) January 3, 2012; published electronically May 31, 2012. This work was supported by the DST-CNPq Indo-Brazil Project DST/INT/Brazil/RPO-05/2007 (grant 490795/2007-2) and award KUK-C1-013-04 made by KAUST.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.